Born–Infeld Gravity from the MacDowell–Mansouri Action and Its Associated $${\varvec{\beta }}$$ β -Term

Abstract

In this work a generalization of a Born–Infeld theory of gravity with a topological $$\beta $$ -term is proposed. These type of Born–Infeld actions were found from the theory introduced by MacDowell and Mansouri. This theory known as MacDowell–Mansouri (MM) gravity was one of the first attempts to construct a gauge theory of gravitation, and within this framework it was introduced in the action a topological $$\beta $$ -term relevant for quantization purposes in an analogous way as in Yang–Mills theory. By the use of the self-dual and antiself-dual actions of MM gravity, we further define a Born–Infeld gravity generalization corresponding to MM gravity with the $$\beta $$ -term.